Problem: Solve for $x$ and $y$ using elimination. $\begin{align*}-5x+9y &= 9 \\ 5x+6y &= 6\end{align*}$
Solution: We can eliminate $x$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $15y = 15$ Divide both sides by $15$ and reduce as necessary. $y = 1$ Substitute $1$ for $y$ in the top equation. $-5x+9( 1) = 9$ $-5x+9 = 9$ $-5x = 0$ $x = 0$ The solution is $\enspace x = 0, \enspace y = 1$.